This is acutally easier than it looks. I just had the same problem with a cloudy film starting to form underneath the glass on my older HP 4400C scanner.
First completely remove the hinged top lid by lifting straight up on both long ends of the lid - notice the 2 hinges on the back end of the lid will come straight up and out of the body of the scanner, still attached to the lid.
Next look down inside the 2 hinge holes (on the main body of the scanner where the lid hinges just came out of) and you will see a screw in each hole. Remove both screws using a phillips screwdriver. This will allow the rear end of the scanner to come apart enough so you can now lift it up a few inches to separate it and get your hand inside there to clean the underside of the glass with a soft cloth - BUT JUST REMEMBER THE FRONT END OF THE SCANNER WILL STILL BE CONNECTED, so don't pull it too far apart because it could snap and break something that is still holding the front end together. (I could not figure out how to separate the front end piece, and then I realized I didn't have to).
So on the rear end of the scanner, now carefully pull the light upper colored plastic apart from the lower dark plastic just enough so you can get your hand inside the compartment and use a soft cloth to clean the underside of the glass. I just used a small piece of an old cotton t-shirt with a couple little dabs of water on it and then just kept rubbing the dirty areas on the underside of the glass over and over until all the dust film/streaks disappeared and the glass was once again clean and all clear.
Then gently lower the glass back down and line up the plastic pieces together on the rear end and put the 2 screws back in the hinge holes, and then reinsert the hinges in their slots and lower the lid back on top of the scanner glass and it is ready to go again !!
Hope this works for you like it did for me.
TIM, February 2010
